For a description of an Admiralty Fire Control Table in action: Cooper, Arthur. "A Glimpse at Naval Gunnery". Ahoy: Naval, Maritime, Australian History.
The increasing range of the guns also forced ships to create very high observation points from which optical rangefinders and artillery spotters could see the battle. The need to spot artillery shells was one of the compelling reasons behind the development of naval aviation and early aircraft were used to spot the naval gunfire points of impact. In some cases, ships launched manned observation balloons as a way to artillery spot. Even today, artillery spotting is an important part of directing gunfire, though today the spotting is often done by unmanned aerial vehicles. For example, during Desert Storm, UAVs spotted fire for the Iowa-class battleships involved in shore bombardment.
See for example, the write-up on Fort Andrews in Boston Harbor for a summary of artillery assets and fire control systems typical of these defenses.